In this study, numerical modeling of nonlinear dynamic responses of miniature electromagnetic energy harvesters is reported for multiple impacts using limited amplitude and low-frequency excitations (0.5–3 g, 10–40 Hz). When an external vibration source frequency approaches oscillators’ resonate frequencies (15 Hz and 30 Hz), these oscillators strongly impact onto a stiffer cantilever resulting in a much higher frequency vibration (1 kHz) in accordance with a large frequency up-conversion factor ∼33.3–66.6. The Lorentz force and the nonlinear oscillators together resulted in complicated nonlinear dynamic responses of the cantilever, such as period doubling, superharmonic, or chaotic. Furthermore, the instantaneous generated power of miniature electromagnetic harvester was dramatically enhanced with 3 μW, and the enhancement came from the more the number of oscillators, the lesser the air damping, and appropriate frequencies from external vibration sources. Moreover, the free tip of the cantilever in the system with both of the cube nonlinear oscillators and the linear oscillators were carefully analyzed by the phase portraits to demonstrate its dynamic responses behavior.
JungSMYunKS. Energy-harvesting device with mechanical frequency-up conversion mechanism for increased power efficiency and wideband operation. Appl Phys Lett2010; 96: 111906–111906.
2.
FanKQChangJWet al.Design and development of a multipurpose piezoelectric energy harvester. Energy Convers Manage2015; 96: 430–439.
3.
CamardaARomaniAet al.A 32 mV/69 mV input voltage booster based on a piezoelectric transformer for energy harvesting applications. Sensors Actuat A2015; 232: 341–352.
4.
UmedaMNakamuraKUehaS. Analysis of the transformation of mechanical impact energy to electric energy using piezoelectric vibration. Jpn J Appl Phys1996; 35: 3267–3273.
5.
GuL. Low-frequency piezoelectric energy harvesting prototype suitable for the MEMS implementation. Microelectronics J2011; 42: 277–282.
6.
KimSBParkHet al.Comparison of MEMS PZT cantilevers based on d(31) and d(33) modes for vibration energy harvesting. J Microelectromech Syst2013; 22: 26–33.
7.
ZengZRenBet al.Excellent performances of energy harvester using cantilever driving double-clamped 0.7Pb(Mg1/3Nb2/3)O-3-0.3PbTiO(3) plates and symmetric middle-stops. Appl Phys Lett2015; 107: 173502–173502.
8.
Suzuki1YMikiDet al.A MEMS electret generator with electrostatic levitation for vibration-driven energy-harvesting applications. J Micromech Microeng2010; 20: 104002–104002.
9.
LinJZhuJXet al.Two-cavity MEMS variable capacitor for power harvesting. J Micromech Microeng2012; 22: 065003–065003.
10.
de QueirozACM. Electrostatic energy harvesting using capacitive generators without control circuits. Analog Integr Circuits Signal Process2015; 85: 57–64.
11.
YuksekNSFengZCAlmasriM. Broadband electromagnetic power harvester from vibrations via frequency conversion by impact oscillations. Appl Phys Lett2014; 105: 113902–113902.
12.
RahimiAZorluOet al.An electromagnetic energy harvesting system for low frequency applications with a passive interface ASIC in standard CMOS. Sensors Actuat A2012; 188: 158–166.
13.
WickenheiserAMGarcisE. Broadband vibration-based energy harvesting improvement through frequency up-conversion by magnetic excitation. Smart Mater Struct2010; 19: 065020–065020.
14.
CarusoG. Broadband energy harvesting from vibrations using magnetic transduction. J Vib Acoust-Trans ASME2015; 137: 064503–064503.
15.
KulahHNajafiK. Energy scavenging from low-frequency vibrations by using frequency up-conversion for wireless sensor applications. IEEE Sens J2008; 8: 261–268.
16.
ChallaVRPrasadMGet al.A vibration energy harvesting device with bidirectional resonance frequency tenability. Smart Mater Struct2008; 17: 015035–015035.
17.
YamamotoKFujitaTet al.A design of mechanical frequency converter linear and non-linear spring combination for energy harvesting. PowerMEMS2014; 557: 012065–012065.
18.
MahmoudiSKacemNBouhaddiN. Enhancement of the performance of a hybrid nonlinear vibration energy harvester based on piezoelectric and electromagnetic transductions. Smart Mater Struct2014; 23: 075024–075024.
19.
AbedIKacemNet al.Multi-modal vibration energy harvesting approach based on nonlinear oscillator arrays under magnetic levitation. Smart Mater Struct2016; 25: 2–2.
20.
ZhuJXLinJet al.Dynamic analysis and phenomena of MEMS capacitive power harvester subjected to low frequency excitation. Nonlinear Dyn2015; 79: 673–688.
21.
LinJZhuJXet al.Surface micromachined MEMS capacitors with dual-cavity for energy harvesting. J Microelectromech Syst2013; 22: 1459–1469.
22.
Costache F, Pawlik B and Rieck A. Development of a compact, low-frequency vibration, piezoelectric MEMS energy harvester. In: Proceedings of Eurosensors 2017, Paris, France, 3–6 September 2017, pp.588(1–5).
23.
Galchev T, Mccullagh J, et al. Harvesting traffic-induced bridge vibrations. In: Transducers’11, Beijing, China, 5–9 June 2011, pp.1661–1664.
24.
Conchouso D, Arevalo A, et al. Simulation of SU-8 frequency-driven scratch drive actuators. In: UKSim 15th international conference on computer modelling and simulation, Cambridge, UK, 10–12 April 2013.
25.
GeCCretuE. MEMS transducers low-cost fabrication using SU-8 in a sacrificial layer-free process. J Micromech Microeng2017; 27: 045002(1–11)–045002(1–11).
JohnsonKLKendallKRobertsAD. Surface energy and the contact of elastic solids. Proc R Soc Lond Ser A1971; 324: 301–313.
28.
HalimMAParkJY. A frequency up-converted electromagnetic energy harvester using human hand-shaking. J Phys: Conf Ser2013; 476: 012119(1–5)–012119(1–5).
29.
JayadeepUBBobjiMS. Energy loss due to adhesion during the impact of elastic spheres. Procedia Eng2017; 173: 238–243.
30.
BarbaraBOKrzysztofCTomaszK. Dynamics of a two-degree-of-freedom cantilever beam with impacts. Chaos Solitons Fract2009; 40: 1991–2006.
31.
SerwetaWOkolewskiAet al.Lyapunov exponents of impact oscillators with Hertz’s and Newton’s contact models. Int J Mech Sci2014; 89: 194–206.
32.
GandhiPSVyasV. On the dynamics of tapered vibro-impacting cantilever with tip mass. J Mech Sci Technol2017; 31: 63–73.
33.
YangBLeeCet al.Electromagnetic energy harvesting from vibrations of multiple frequencies. J Micromech Microeng2009; 19: 035001(1–8)–035001(1–8).
34.
DennisJOAhmedAYet al.Modelling and simulation of the effect of air damping on the frequency and quality factor of a CMOS-MEMS resonator. Appl Math Inf Sci2015; 9: 729–737.
35.
ChungTYYangCSet al.Investigating excitation-dependent and fringe-field effects of electromagnet and permanent-magnet phase shifters for a crossed undulator. Nucl Instrum Methods Phys Res A2017; 850: 72–77.
36.
MaJPSunYet al.Dynamics and collapse in a power system model with voltage variation: The damping effect. PLOS One2016; 11: 1–28.
37.
GeCFSutherlandS. Application of experimental modal analysis to determine damping properties for stacked corrugated boxes. Math Prob Eng2013; 651348: 1–8.
